Vorhersage bei stochastischen Prozessen mit linearem Regressionsanteil.I

Abstract

The author considers models of the form containing as special cases the finite dimensional regression models. Let β(μ) be an unknown functionfor u ∈ U ⊆ R 1 and x(s, u) be known functions being integrable relative to u.Let further be . Knowing a realisation of the process y t, t ∈ T the process y s, s ∈ S shall ne predicated. As risque of a prediction p(s) of y s we utilize Under certain propositions the author determines a best linear homogeneous resp, a best linear homogeneous unbiased resp a best linear inhomogeneous prediction using functional analytical methods without demanding regularity properties of the covariance operator from ϵt.